When changing the id of the entity on the shoulder of a player (changing the parrot by something else) you always see a parrot appear, but when you jump, it is not a parrot that falls. The parrots are also visible on the shoulder even if they add invisible potion effect.
1. Don't put multiple issues in 1 report.
2. (Always parrot) Invalid as it can only be achieved using third party tools.
3. (Invisibility) Already reported.